Speaking on BBC Radio 4 Today programme, he said: "I always take the view that anyone whether it is an individual or an organisation is innocent until proven guilty.

"We have been very clear that we will watch very carefully what happens in the police investigation and if there is any evidence of systemic fraud in our relationship with A4E we will not hesitate to terminate our relationship with them."

His comments come a day after Mrs Harrison, who was criticised for taking £8.6 million in a dividend from a company dependent on the taxpayer, quit as a government adviser.

She said she did not want the "current media environment to distract from the very important work with troubled families".

It also came as it emerged the company was accused of sending unemployed clients to work for nothing in its own offices.

A4e has been under the spotlight since four former employees were arrested and an MP pledged to hand a dossier on the company to the Serious Fraud Office.

The Prime Minister’s spokesman said Mrs Harrison, the chairman and founder of A4e, had made her own decision to step down and had not been pushed to resign.

“We respect her decision and we thank her for her contribution,” the spokesman said.

A4e is paid by the Government to find work for unemployed people. However, in recent days, it has been accused of allowing its employees falsely to claim people have been placed in work and sending the unemployed to work for free in its own offices.

Sainsbury’s has cut all ties with A4e, after finding the company had persuaded some of its store managers that it was authorised to provide jobless workers for unpaid work experience.

A Sainsbury’s spokesman said: "We have constantly reminded A4e that they should not place workers in our stores and that we wanted to stick within our own scheme. However, people from A4e managed to convince some of our store managers that their scheme had been authorised by our head office. This was finished as soon as this was found out.”

A4e claims the current police investigation centres solely on four former employees. But police sources say that the investigation goes further than the four arrested people and is looking at the “wider practices” of the company.

The police investigation is being overseen by Thames Valley Police, but Fiona Mactaggart MP has written to the SFO asking for an inquiry.

Sources said that the SFO’s resources would mean they would be well placed to take over the Thames Valley investigation.

The Prime Minister has made it clear A4e is able to bid for new contracts while a "thorough" police investigation is still going on.

But last night, Paul Blomfield, Labour MP for Sheffield West, called for the Government to suspend new negotiations and “publish all details of current and pending contracts with A4e”.

A4e is in a consortium that is one of three preferred bidders for a multi-million pound "community payback" contract due to be awarded by the Ministry of Justice this year.

Liam Byrne MP, Labour's Shadow Work and Pensions Secretary, said: "Emma Harrison has done the right thing. But this is not the end – it’s the start of the real questions about the Government's back to work contracts which are costing millions but are simply not getting enough people into jobs."